3.12.1 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{x (b+a x^3)} \, dx\)
  3.12.2 \(\int \frac {\sqrt [4]{b x^3+a x^4}}{x} \, dx\)
  3.12.3 \(\int \frac {(-b+a x) \sqrt [4]{b x^3+a x^4}}{x (b+a x)} \, dx\)
  3.12.4 \(\int \frac {-1+3 x^4}{(1-x+x^4) \sqrt [3]{x^2+x^6}} \, dx\)
  3.12.5 \(\int \frac {1}{\sqrt [4]{-b x^2+a x^4} (-b+a x^8)} \, dx\)
  3.12.6 \(\int \frac {1}{\sqrt [4]{-b x^2+a x^4} (-b+a x^8)} \, dx\)
  3.12.7 \(\int \frac {-b+a x^8}{x^2 (b+a x^4)^{3/4}} \, dx\)
  3.12.8 \(\int \frac {x^5 (-4 b+5 a x^2)}{\sqrt [4]{-b+a x^2} (b-b x^8+a x^{10})} \, dx\)
  3.12.9 \(\int \frac {1}{\sqrt [3]{x^2+x^3}} \, dx\)
  3.12.10 \(\int \frac {a-3 b+2 x}{\sqrt [4]{(-a+x) (-b+x)} (-a^3+b d-(-3 a^2+d) x-3 a x^2+x^3)} \, dx\)
  3.12.11 \(\int \frac {(a-3 b+2 x) (a^2-2 a x+x^2)}{((-a+x) (-b+x))^{3/4} (-b+a^3 d+(1-3 a^2 d) x+3 a d x^2-d x^3)} \, dx\)
  3.12.12 \(\int \frac {-1-2 (-1+k) x+k x^2}{\sqrt [4]{(1-x) x (1-k x)} (-1+(d+3 k) x-(d+3 k^2) x^2+k^3 x^3)} \, dx\)
  3.12.13 \(\int \frac {\sqrt {1+6 x^2+x^4}}{x (1+x^2)} \, dx\)
  3.12.14 \(\int \frac {(-1+x^2) \sqrt [4]{-1+2 x^2+2 x^4}}{x^2 (-1+2 x^2)} \, dx\)
  3.12.15 \(\int \frac {1}{\sqrt [4]{b+a x^4} (2 b+a x^4)} \, dx\)
  3.12.16 \(\int \frac {\sqrt [4]{-b x^2+a x^4}}{x^2} \, dx\)
  3.12.17 \(\int \frac {1}{\sqrt [4]{-b x^2+a x^4} (a+b x^8)} \, dx\)
  3.12.18 \(\int \frac {1}{\sqrt [4]{-b x^2+a x^4} (a+b x^8)} \, dx\)
  3.12.19 \(\int \frac {(-1+x) \sqrt {x+\sqrt {1+x}}}{\sqrt {1+x}} \, dx\)
  3.12.20 \(\int \frac {x \sqrt {x+\sqrt {1+x}}}{\sqrt {1+x}} \, dx\)
  3.12.21 \(\int \sqrt {1+x} \sqrt {x+\sqrt {1+x}} \, dx\)
  3.12.22 \(\int \frac {1+\sqrt {1+x^2}}{\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.12.23 \(\int \frac {\sqrt {1-4 x+x^2}+(1-4 x+x^2)^{3/2}}{\sqrt {1-4 x+x^2}+(1-4 x+x^2)^{3/2}-(1-4 x+x^2)^{5/2}} \, dx\)
  3.12.24 \(\int \frac {x^2}{\sqrt {-b x+a^2 x^2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.12.25 \(\int \frac {a^2 b-a (2 a+b) x+3 a x^2-x^3}{x (-b+x) \sqrt {x (-a+x) (-b+x)} (a+(-1-b d) x+d x^2)} \, dx\)
  3.12.26 \(\int \frac {(1+x^3)^{2/3}}{x} \, dx\)
  3.12.27 \(\int \frac {(-b+2 a x^2) \sqrt [4]{b x^2+a x^4}}{b+a x^2} \, dx\)
  3.12.28 \(\int \frac {(-1+x^4) \sqrt {1+x^2+x^4} (1+x^2+3 x^4+x^6+x^8)}{(1+x^4)^3 (1-x^2+x^4)} \, dx\)
  3.12.29 \(\int \frac {(1+x^6) (-1+x^3+x^6) \sqrt {1+x^{12}}}{x^7 (-1-x^3+x^6)} \, dx\)
  3.12.30 \(\int \sqrt {d+c \sqrt {b+a x}} \, dx\)
  3.12.31 \(\int \frac {1+2 x^2}{x (1+x^2)^{2/3}} \, dx\)
  3.12.32 \(\int \frac {x}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^2 x^2)} \, dx\)
  3.12.33 \(\int \frac {1+x}{(-1+2 x+x^2) \sqrt {-x+x^3}} \, dx\)
  3.12.34 \(\int \frac {-x+x^2}{(-1+2 x+x^2) \sqrt {-x+x^3}} \, dx\)
  3.12.35 \(\int \frac {3+x^2}{\sqrt [3]{1+x^2} (1+x^2+x^3)} \, dx\)
  3.12.36 \(\int \frac {x}{(-1+x^3) (-1+2 x^3)^{2/3}} \, dx\)
  3.12.37 \(\int \frac {(-1-2 (-1+k) x+k x^2) (1-2 k x+k^2 x^2)}{((1-x) x (1-k x))^{3/4} (-d+(1+3 d k) x-(1+3 d k^2) x^2+d k^3 x^3)} \, dx\)
  3.12.38 \(\int \frac {-1+x^4}{\sqrt {-x+x^3} (1+x^4)} \, dx\)
  3.12.39 \(\int \frac {-1+x^2}{(1+x+x^2) \sqrt [3]{x^2+x^4}} \, dx\)
  3.12.40 \(\int \frac {(-2 b+a x^4) (b+a x^4)^{3/4}}{x^8} \, dx\)
  3.12.41 \(\int \frac {(-b+a x^4)^{3/4} (-b+2 a x^4)}{x^8} \, dx\)
  3.12.42 \(\int \frac {(-q+p x^2) (a q+b x+a p x^2) \sqrt {q^2+p^2 x^4}}{x^4} \, dx\)
  3.12.43 \(\int \frac {-1+2 x^3}{(1+x+x^3) \sqrt [3]{x^2+x^5}} \, dx\)
  3.12.44 \(\int \frac {2+3 x^5}{(-1+x^2+x^5) \sqrt [3]{-x+x^6}} \, dx\)
  3.12.45 \(\int \frac {\sqrt {-1+x^6} (-1+2 x^6)^2}{x^4 (-1+4 x^6)} \, dx\)
  3.12.46 \(\int \frac {1+x^4}{\sqrt [4]{-1+x^4} (1+x^4+x^8)} \, dx\)
  3.12.47 \(\int \frac {-1+2 x^4}{\sqrt [4]{-1+x^4} (-2-x^4+2 x^8)} \, dx\)
  3.12.48 \(\int \frac {-1+x^4+2 x^8}{\sqrt [4]{-1+x^4} (1-x^4+x^8)} \, dx\)
  3.12.49 \(\int \frac {1}{\sqrt [4]{b x^2+a x^4} (-2 b+a x^8)} \, dx\)
  3.12.50 \(\int \frac {1}{\sqrt [4]{b x^2+a x^4} (-2 b+a x^8)} \, dx\)
  3.12.51 \(\int \frac {(4+x^5) \sqrt [4]{-2+x^4+2 x^5} (2-4 x^5+x^8+2 x^{10})}{x^{10} (-1+x^5)} \, dx\)
  3.12.52 \(\int \frac {1+x^{12}}{\sqrt {1+x^4} (-1+x^{12})} \, dx\)
  3.12.53 \(\int \frac {\sqrt {1-x^6} (1+2 x^6) (1+x^2-x^4-2 x^6-x^8+x^{12})}{(-1+x^6) (-1+2 x^6-3 x^{12}+x^{18})} \, dx\)
  3.12.54 \(\int \frac {x^2-\sqrt {1+x^2}}{\sqrt {1+\sqrt {1+x^2}}} \, dx\)
  3.12.55 \(\int \frac {1}{(-1+x) \sqrt [3]{2-2 x+x^2}} \, dx\)
  3.12.56 \(\int \frac {1}{(1+x) \sqrt [3]{2+2 x+x^2}} \, dx\)
  3.12.57 \(\int \frac {(-1+x^3)^{2/3}}{x} \, dx\)
  3.12.58 \(\int \frac {3+x^2}{\sqrt [3]{1+x^2} (-1-x^2+x^3)} \, dx\)
  3.12.59 \(\int \frac {-2-(-1+k) (1+k) x+2 k^2 x^2}{\sqrt [4]{(1-x^2) (1-k^2 x^2)} (-1+d-(3+d) x-(3+d k^2) x^2+(-1+d k^2) x^3)} \, dx\)
  3.12.60 \(\int \frac {-2+(-1+k) (1+k) x+2 k^2 x^2}{\sqrt [4]{(1-x^2) (1-k^2 x^2)} (1-d-(3+d) x+(3+d k^2) x^2+(-1+d k^2) x^3)} \, dx\)
  3.12.61 \(\int \frac {\sqrt [4]{-1+x^4}}{x} \, dx\)
  3.12.62 \(\int \frac {\sqrt {-x+x^4}}{-b+a x^3} \, dx\)
  3.12.63 \(\int \frac {1}{(-1+x^4) \sqrt [4]{-x^2+x^4}} \, dx\)
  3.12.64 \(\int \frac {\sqrt [4]{-x^3+x^4}}{-1-2 x+x^2} \, dx\)
  3.12.65 \(\int \frac {\sqrt [4]{-x^3+x^4}}{-1-2 x+x^2} \, dx\)
  3.12.66 \(\int \frac {x^6}{(-b+a x^4)^{3/4}} \, dx\)
  3.12.67 \(\int \frac {(-b+a x^4) \sqrt [4]{b+a x^4}}{x^2} \, dx\)
  3.12.68 \(\int \frac {(-1+x^3)^{2/3} (2+x^3)}{x^6 (-4-2 x^3+x^6)} \, dx\)
  3.12.69 \(\int \frac {(-1+x^3)^{2/3} (2+x^3)}{x^6 (-4-2 x^3+x^6)} \, dx\)
  3.12.70 \(\int \frac {(-1+x^3)^{2/3} (4-2 x^3+x^6)}{x^6 (-8+4 x^3+x^6)} \, dx\)
  3.12.71 \(\int \frac {(-1+x^3)^{2/3} (4-2 x^3+x^6)}{x^6 (-8+4 x^3+x^6)} \, dx\)
  3.12.72 \(\int \frac {(-1+x^3)^{2/3} (2-2 x^3+x^6)}{x^6 (-4+4 x^3+x^6)} \, dx\)
  3.12.73 \(\int \frac {(-1+x^3)^{2/3} (2-2 x^3+x^6)}{x^6 (-4+4 x^3+x^6)} \, dx\)
  3.12.74 \(\int \frac {2+x^4}{\sqrt [4]{-1+x^4} (-2+x^8)} \, dx\)
  3.12.75 \(\int \frac {-b+a x^8}{x^6 (b+a x^4)^{3/4}} \, dx\)
  3.12.76 \(\int \frac {\sqrt {x}}{(-1+x) \sqrt {-\sqrt {x}+x}} \, dx\)
  3.12.77 \(\int \frac {1}{x^3 (1+x^2)^{2/3}} \, dx\)
  3.12.78 \(\int \frac {(1+x^2)^{2/3}}{x^3} \, dx\)
  3.12.79 \(\int \frac {(1+x^2)^{2/3}}{x} \, dx\)
  3.12.80 \(\int \frac {(3+4 x) \sqrt {x+2 x^2-2 x^4}}{(1+2 x) (1+2 x+x^3)} \, dx\)
  3.12.81 \(\int \frac {(1+x^4)^{2/3}}{x} \, dx\)
  3.12.82 \(\int \frac {\sqrt [3]{-1+x^4} (3+x^4)}{x^2 (-1-x^3+x^4)} \, dx\)
  3.12.83 \(\int \frac {x^2 (4+x^3)}{(1+x^3)^{3/4} (1+x^3+x^4)} \, dx\)
  3.12.84 \(\int \frac {x^2}{(-b+a x^4)^{3/4} (b+a x^4)} \, dx\)
  3.12.85 \(\int \frac {1}{\sqrt [4]{-b+a x^4} (b+a x^4)} \, dx\)
  3.12.86 \(\int \frac {-a^2 b+a (2 a+b) x-3 a x^2+x^3}{\sqrt {x (-a+x) (-b+x)} (-a^2+2 a x+(-1+b^2 d) x^2-2 b d x^3+d x^4)} \, dx\)
  3.12.87 \(\int \frac {1+k^2 x^4}{\sqrt {(1-x^2) (1-k^2 x^2)} (-1+k^2 x^4)} \, dx\)
  3.12.88 \(\int \frac {x (-1+k x) (-1+(-1+2 k) x)}{\sqrt [3]{(1-x) x (1-k x)} (-1+(4-c) x+(-6+b+2 c+c k) x^2+(4-c-2 b k-2 c k) x^3+(-1+c k+b k^2) x^4)} \, dx\)
  3.12.89 \(\int \frac {(1+x^5)^{2/3}}{x} \, dx\)
  3.12.90 \(\int \frac {(1+x^6)^{2/3}}{x} \, dx\)
  3.12.91 \(\int \frac {(1-x^2+2 x^4) \sqrt {1-x^2-x^4-x^6}}{(-1+x^2) (1+x^2) (-1+x^4+x^6)} \, dx\)
  3.12.92 \(\int \frac {\sqrt [3]{-1+x^8} (3+5 x^8)}{x^2 (-1-x^3+x^8)} \, dx\)
  3.12.93 \(\int \frac {(2+x^8) \sqrt {4-2 x^8+x^{16}}}{x^9} \, dx\)
  3.12.94 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{1-\sqrt {1+x}} \, dx\)
  3.12.95 \(\int \frac {\sqrt {c+\sqrt {b+a x}}}{d-\sqrt {b+a x}} \, dx\)
  3.12.96 \(\int (b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}} \, dx\)
  3.12.97 \(\int \frac {1}{x+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.12.98 \(\int \frac {1}{x+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.12.99 \(\int \frac {1}{(-2+x) \sqrt [3]{-4-4 x+x^2}} \, dx\)
  3.12.100 \(\int \frac {-1+k x^2}{(a+b x) \sqrt {(1-x) x (1-k x)} (b+a k x)} \, dx\)